System and method for training with a virtual apparatus

ABSTRACT

A method and system of training in conjunction with a computer animation executed by a computing environment is described. The method includes recognizing a task to be performed in the computer animation, recognizing a problem, displayed in the computer animation, to accomplish the task, and solving the problem by manipulation of a virtual apparatus having virtual components displayed in the computer animation. The virtual components are manipulated by a student or user desiring to learn. The student is taught to understand logically consistent goals by using the virtual apparatus and without language interaction. Rules and properties for a subject area are modeled to the student by the virtual apparatus without language interaction. The student is taught to operate the virtual apparatus without language interaction. The student is requested to operate the virtual apparatus to reach goals in a sequence of problems having progressive difficulty and without language interaction.

RELATED APPLICATIONS

This is a continuation of copending application Ser. No. 11/218,282 filed Sep. 1, 2005, which is hereby incorporated by reference in its entirety.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to training, and more particularly, to use a virtual apparatus via a computer animation executed by a computer environment without needing language interaction.

2. Description of the Related Technology

In the 1970's Dr. Gordon Shaw, a founder of the M.I.N.D. Institute, pioneered the area of spatial temporal reasoning and noted that American education had historically overly focused on the LA (Language-Analytical) portion of human reasoning, and substantially overlooked ST (Spatial-Temporal) reasoning as a learning mode. Since then, our understanding of how the brain works, and how learning takes place has increased. Gaining this understanding is an ongoing dynamic process.

Unfortunately, while a doctor from the mid 19^(th) century would be lost, and a menace, both to himself, and to patients, in a 2005 United States hospital, a school teacher from 1850 would likely feel at home in today's classrooms, once she recovered from fainting at the girl's customary attire. While the world has dramatically changed in the last 150 years, teaching methods have not kept up. Generally, computing power is relegated to an adaptive and adjunct role, rather than to develop new learning paradigms. This state of events is unsatisfactory, and cannot be tolerated.

Admittedly, education systems face daunting challenges. Cultural and linguistic homogeneity have sharply decreased. In the United States, teachers can no longer presume that all students speak English. In some school districts, numerous languages are spoken at children's homes. The historical demand that children acclimate to America, and learn only English, has diminished. Many students lack effective family support systems. Television, video games, and computer games, compete with homework for students after school attention, and the federal government, through partially or totally unfunded mandates, requires schools to do more, with fewer resources.

Additionally, early childhood education, education of those for who English is a second language, and educating the learning disabled are growth areas. While preschool children may, or may not, understand spoken English, there is no reason to presume that they read English. Additionally, many people, regardless of age, are illiterate. As the supply of good jobs for those having little formal education dries up, the need for creative educational paradigms increases.

While infrastructure is becoming available, this alone cannot solve the problem. Computers offer wondrous opportunities to expand learning, but a paradigm to generate a quantum leap in educational results is lacking. True, students can now do on-line research, and create computerized presentations for class instead of typed or handwritten reports. They can search through billions of references by using Internet search programs. However, this is merely incrementally improving an existing educational process many view as grossly inadequate. Regardless, we have not addressed how to help students reason and think. As previously mentioned the language gap in schooling is a continuing problem.

Using manipulatives in teaching mathematics began at least in the 1980's, and possibly well before. This accesses different reasoning pathways, (Spatial-Temporal) than does dealing merely with abstractions. Virtual manipulatives have been created as computer-generated images. However, these manipulatives have merely been used as an adjunct or supplement to spoken or textual language, rather than a replacement therefore. Further, virtual manipulative lack important aspects of real world objects.

In the real world, objects are subject to physical laws learned even by toddlers. For example, generally an object, when released, neither hovers, nor rises, but falls to the ground. An object at rest remains so unless acted upon. A hole is something to fall into. Free objects above the ground fall. In general, objects follow predictable rules. While a virtual manipulative looks like the real thing, it need not behave so, unless placed in a logical construct where it is constrained. We define such a constrained virtual manipulative as a virtual apparatus.

Traditionally, students learn subjects via the written or spoken word. By definition, language translates the concrete into the abstract. Therefore, in all such learning, language ability is a choke point or limiting factor. Such a limiting factor is often unnecessary. Consider the problem, 2+2=4. Placing two blocks next to two blocks provides four blocks, without any resort to language or symbolism. Imagine a construct where selecting two additional blocks creates a successful result.

While bridging the language gap at some point likely needs to be done, no a priori reason exists for all instruction to be language based. A chemistry or physics experiment is NOT language based, but has real world results. Similar geometric experiments exist. When imparting learning from a subject, or discipline, conveyable primarily or purely through physical means, such as virtual apparati, introducing language abstractions in the learning process is an unnecessary complicating, and hindering factor.

Originally, counting was by pebbles, twigs, or other physical means. Additionally, subtraction, algebra, story problems, geometry, and many other subjects can be taught without using language. This is beneficial for various reasons. First, as the problem is inherently physical, there is no underlying reason to convert the problem from the physical realm into the abstract realm. Secondly, if the problem remains in the physical realm, the realm of spatial temporal reasoning, rather than the realm of language—analytical reasoning, then language skills are no longer either a limiting or a complicating factor. Third, if the problem is language independent, the students' English skills are irrelevant.

Imagine a classroom where 25 children who speak seven different languages can solve the same problem from the same computer program. A single version of a single problem is comprehensible and solvable to speakers of any language, or none at all. The same logical rules would be applicable to each subject. Reasoning, logic, math, science, and more, all taught without need for textual symbols.

Admittedly, a language transition would be required to transfer the learning skills from this logical construct into the broader logic of the physical world. However, this process is primarily relabling previously learned facts and thought processes, and adapting thought processes to a broader perspective.

A need exists for a paradigm for teaching subjects using physical representations, such as a virtual apparatus, where using language is unnecessary, and then addressing the language gap after substantial learning occurs. Likewise, a need exists for methods of teaching processes that do not rely on unnecessary single or double translations between concrete and abstract thought processes. Further, a need exists for software that enables this new educational method.

SUMMARY OF CERTAIN INVENTIVE ASPECTS

Certain embodiments include a computer based learning method, and implementing software that implements a new learning paradigm. This method of learning/method of teaching implements advances in the understanding of spatial temporal (ST) reasoning to allow students to learn without relying on language or language analytical (LA) reasoning.

Accordingly, this method applies to any subject matter where ST reasoning applies. This method is particularly applicable for use with students having learning disabilities, limited language skills, or limited English skills in English based learning environments.

In one embodiment of the invention there is a method of training in conjunction with a computer animation executed by a computing environment, the method comprising creating a logical construct including establishing a set of consistent rules, providing a virtual apparatus with virtual components that are manipulated by a user being trained, teaching the user to understand logically consistent goals by using the virtual apparatus and without language interaction, modeling properties and the set of consistent rules for a subject area to the user by the virtual apparatus without language interaction, teaching the user to operate the virtual apparatus without language interaction, requesting the user to operate the virtual apparatus to reach goals in a sequence of problems having progressive difficulty and without language interaction.

The method may additionally comprise selecting an appropriate subject matter area, and selecting a sequence of problems according to the selected subject matter area. The method may additionally comprise establishing error tolerances for the problems. The method may additionally comprise determining if the user has mastered a subject area sub-category. The method may additionally comprise introducing language elements to the user in conjunction with the computer animation if the user has mastered a subject area sub-category. The language elements may comprise numerals and/or labels.

In another embodiment of the invention there is a method of training in conjunction with a computer animation executed by a computing environment, the method comprising recognizing a task to be performed in the computer animation, recognizing a problem, displayed in the computer animation, to accomplish the task, and solving the problem by manipulation of a virtual apparatus executing in the computing environment.

The method may additionally comprise animating positive feedback to a user if the problem was solved correctly. Animating positive feedback may comprise showing the user why the problem was solved correctly. The method may additionally comprise introducing language elements to the user in conjunction with the computer animation. The language elements may comprise numerals and/or labels. The language elements may be added to the display near the virtual apparatus. The language elements may be added to the display in place of portions of the virtual apparatus. The method may additionally comprise solving a new problem in a language-analytic environment wherein the new problem and the solved problem are related to a concept being taught. The method may additionally comprise animating negative feedback to a user if the problem was not solved correctly. Animating negative feedback may comprise showing the user why the problem was not solved correctly.

The method of training may be self-contained. Solving the problem may utilize spatial temporal reasoning. The method may additionally comprise designating a task to be performed in the computer animation. The computer animation may include only essential images. The positive feedback computer animation may include only essential output. The negative feedback computer animation may include only essential output.

In another embodiment of the invention there is a method of training in conjunction with a computer animation executed by a computing environment, the method comprising recognizing a task to be performed in the computer animation, recognizing a problem, displayed in the computer animation, to accomplish the task, and solving the problem using a virtual apparatus with virtual components displayed in the computer animation. The method of training may be without intervention and instruction by a teacher.

In another embodiment of the invention there is a system for training, the system comprising a computing environment executing a computer animation, means for recognizing a task to be performed in the computer animation, means for recognizing a problem, displayed in the computer animation, to accomplish the task, and a virtual apparatus with virtual components displayed in the computer animation for solving the problem.

In another embodiment of the invention there is a computer readable medium containing software that, when executed, causes the computer to perform the acts of recognizing a task to be performed in a computer animation, recognizing a problem, displayed in the computer animation, to accomplish the task, and solving the problem using a virtual apparatus with virtual components displayed in the computer animation.

In another embodiment of the invention there is a method of training, the method comprising providing a virtual apparatus with virtual components that are manipulated by a user being trained, and teaching the user to understand logically consistent goals by using the virtual apparatus and without language interaction.

In another embodiment of the invention there is a computer readable medium containing software that, when executed, causes the computer to perform the acts of providing a virtual apparatus with virtual components that are manipulated by a user being trained, and teaching the user to understand logically consistent goals by using the virtual apparatus and without language interaction.

In another embodiment of the invention there is a method of training, the method comprising providing a virtual apparatus with virtual components that are manipulated by a user being trained, and modeling rules and properties for a subject area to the user by the virtual apparatus without language interaction.

In another embodiment of the invention there is a computer readable medium containing software that, when executed, causes the computer to perform the acts of providing a virtual apparatus with virtual components that are manipulated by a user being trained, and modeling rules and properties for a subject area to the user by the virtual apparatus without language interaction.

In another embodiment of the invention there is a method of training, the method comprising providing a virtual apparatus with virtual components that are manipulated by a user being trained; and teaching the user to operate the virtual apparatus without language interaction.

In another embodiment of the invention there is a computer readable medium containing software that, when executed, causes the computer to perform the acts of providing a virtual apparatus with virtual components that are manipulated by a user being trained, and teaching the user to operate the virtual apparatus without language interaction.

In another embodiment of the invention there is a method of training, the method comprising providing a virtual apparatus with virtual components that are manipulated by a user being trained, and requesting the user to operate the virtual apparatus to reach goals in a sequence of problems having progressive difficulty and without language interaction.

In yet another embodiment of the invention there is a computer readable medium containing software that, when executed, causes the computer to perform the acts of providing a virtual apparatus with virtual components that are manipulated by a user being trained, and requesting the user to operate the virtual apparatus to reach goals in a sequence of problems having progressive difficulty and without language interaction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a high level block diagram of one embodiment of a system for teaching rules for educational games without the use of words.

FIG. 1B is a block diagram of an exemplary problem at a puzzle stage and at a solution stage that can be performed on the system shown in FIG. 1A.

FIGS. 2A and 2B are a top level flowchart of exemplary software processes that can be executed on the system shown in FIG. 1A.

FIG. 3 is a diagram of an exemplary hierarchy of subjects, aspects and puzzles for aid in understanding states 250, 252 and 254 of FIG. 2B.

FIG. 4 is an exemplary flowchart of the process 210 shown in FIG. 2A.

FIG. 5 is an exemplary flowchart of the process 220 shown in FIG. 2A.

FIG. 6 is an exemplary flowchart of the process 230 shown in FIG. 2A.

FIG. 7 is an exemplary flowchart of the process 240 shown in FIG. 2A.

DETAILED DESCRIPTION OF CERTAIN INVENTIVE EMBODIMENTS

The following detailed description of certain embodiments presents various descriptions of specific embodiments of the invention. However, the invention can be embodied in a multitude of different ways as defined and covered by the claims. In this description, reference is made to the drawings wherein like parts are designated with like numerals throughout.

The terminology used in the description presented herein is not intended to be interpreted in any limited or restrictive manner, simply because it is being utilized in conjunction with a detailed description of certain specific embodiments of the invention. Furthermore, embodiments of the invention may include several novel features, no single one of which is solely responsible for its desirable attributes or which is essential to practicing the inventions herein described.

The system is comprised of various modules, tools, and applications as discussed in detail below. As can be appreciated by one of ordinary skill in the art, each of the modules may comprise various sub-routines, procedures, definitional statements and macros. Each of the modules are typically separately compiled and linked into a single executable program. Therefore, the following description of each of the modules is used for convenience to describe the functionality of the preferred system. Thus, the processes that are undergone by each of the modules may be arbitrarily redistributed to one of the other modules, combined together in a single module, or made available in, for example, a shareable dynamic link library.

The system modules, tools, and applications may be written in any programming language such as, for example, C, C++, BASIC, Visual Basic, Pascal, Ada, Java, HTML, XML, or FORTRAN, and executed on an operating system, such as variants of Windows, Macintosh, UNIX, Linux, VxWorks, or other operating system. C, C++, BASIC, Visual Basic, Pascal, Ada, Java, HTML, XML and FORTRAN are industry standard programming languages for which many commercial compilers can be used to create executable code.

A computer or computing device may be any processor controlled device including terminal devices, such as personal computers, workstations, servers, clients, mini-computers, main-frame computers, laptop computers, a network of individual computers, mobile computers, palm-top computers, hand-held computers, set top boxes for a television, other types of web-enabled televisions, interactive kiosks, personal digital assistants, interactive or web-enabled wireless communications devices, mobile web browsers, or a combination thereof. The computers may further possess one or more input devices such as a keyboard, mouse, touch pad, joystick, pen-input-pad, and the like. The computers may also possess an output device, such as a visual display and an audio output. One or more of these computing devices may form a computing environment.

These computers may be uni-processor or multi-processor machines. Additionally, these computers may include an addressable storage medium or computer accessible medium, such as random access memory (RAM), an electronically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), hard disks, floppy disks, laser disk players, digital video devices, compact disks, video tapes, audio tapes, magnetic recording tracks, electronic networks, and other techniques to transmit or store electronic content such as, by way of example, programs and data. In one embodiment, the computers may be equipped with a network communication device such as a network interface card, a modem, or other network connection device suitable for connecting to a communication network. Furthermore, the computers execute an appropriate operating system such as Linux, UNIX, any of the versions of Microsoft Windows, Apple MacOS, IBM OS/2 or other operating system. The appropriate operating system may include a communications protocol implementation that handles all incoming and outgoing message traffic passed over the network

The computers may contain program logic, or other substrate configuration representing data and instructions, which cause the computer to operate in a specific and predefined manner, as described herein. In one embodiment, the program logic may be implemented as one or more object frameworks or modules. These modules may be configured to reside on the addressable storage medium and configured to execute on one or more processors. The modules include, but are not limited to, software or hardware components that perform certain tasks. Thus, a module may include, by way of example, components, such as, software components, object-oriented software components, class components and task components, processes, functions, attributes, procedures, subroutines, segments of program code, drivers, firmware, microcode, circuitry, data, databases, data structures, tables, arrays, and variables.

The method and system applies to teaching a wide variety of disciplines and minimizes or eliminates abstractions or symbols while teaching using constrained virtual manipulatives defined as a virtual apparatus. The constraints require the virtual manipulatives to behave in accordance with easily learned rules. While symbols or abstractions may be added to the displayed puzzles, the crux of the learning is accomplished without having to resort to such abstractions. The method used by certain embodiments comprises three phases.

In one embodiment, the initial phase is a tutorial, which teaches the user how to use the implementing software. The tutorial is fully informative without using written or spoken language. One key technique is impoverishing the visual environment. Consider, for example, the old video game commonly known as PONG which comprised a monochromatic monitor, each player's virtual paddles, and a cathode-ray tube trace which functioned as a virtual ball, which was constrained by the physical constraint that the angle of incidence equaled the angle of reflection. After the user has demonstrated mastery of the tutorial, he or she may proceed to an initial subject matter puzzle.

The method involves creating single and multi-step puzzles, arranged hierarchically. The learning process involves having the user complete a non-textual training stage, and a non-textual learning stage. In one embodiment, the method progresses from non-textual puzzles to puzzles including text to bridge the language gap. The method and software are suitable for all users, as the non-textual learning puzzles and solutions are language independent.

Regardless of the academic discipline, puzzles are solved the same way. Each puzzle constitutes an impassable success path, and comes with a set of possible solutions. Each solution set, and each set member, consists of virtual apparatus. In the preferred embodiment, in accord with learning theory best practices, each solution set member depicts a logically true statement. Ideally, each solution consists of one or more virtual manipulatives. The user selects a possible solution. The software applies the selected solution to the success path. The correct solution makes the success path passable. An incorrect solution leaves the success path impassable. Preferably, user selected incorrect solutions remains visible as user resources. Preferably, additional success indicators are used, such as an animated figure with easily learned movement rules traveling the entire path. Preferably, the software displays only essential information and graphics. The method uses a computer with display, a user controlled input device, and preferably, ways for user identification, score recordation, and score analysis.

Referring to FIGS. 1A and 1B, a system 10 comprises software 12, designed to be used with a computer 13 having a display 14, and a user controlled input device 16. The system 10 teaches students or users 18 a selected academic discipline by means of puzzles 22, where each puzzle 22 comprises an arena 23 which comprises a success path 24, and virtual apparatus 26 controlled by student 18 by means of input device 16. During the presentation of each puzzle 22, virtual apparatus 26 comprises a solution set 28 having potential answers 30. At a puzzle stage 32, success path 24 is impassable. Each puzzle 22 is solved by the student 18 selecting a proper virtual apparatus 26, through input device 16, that when applied to success path 24, changes success path 24 from impassable to passable, changing puzzles 22 from puzzle stage 32 to solution stage 34. Although the description refers to students, it also applies to any user desiring to learn something new.

Software 12 comprises a training component 40 and a puzzle or problem component 42. A language integration component 44 may also be provided as described below. Note that software 12 may allow a puzzle 22 to teach students 18 a part of both puzzle component 42 and language integration component 44. As shown particularly well in Example 1-3 (shown in Appendix C) and Example 1-4 (shown in Appendix D), language skills are introduced in tandem with the already learned spatial-temporal (ST) representations used to teach the applicable concepts. Therefore, student 18 does not require high level language-analytical (LA) skills to identify the previously learned ST skills in the prevalent LA environment. Although the description refers to puzzles, it also applies to any type of problem to be solved.

As also shown by examples 1-1 through 1-7 (shown in the Appendices), ST skills can teach a variety of concepts from the geometric, to fractions, multiplication, ratios, and more. Embedding text seamlessly into previously learned ST skills is believed to both maximize learning and minimize detriments caused by possible language skill deficiencies in students 18.

Training component 40 presents students 18 with puzzles 22 which teach students 18 the rules of the logical construct selected for the system 10. Mastery of training component 40 allows student access to puzzle component 42, as described below.

In certain embodiments, puzzle component 42 comprises puzzles 22 which are organized into bins and levels. Puzzles 22 teach students 18 through the utilization of ST reasoning.

Referring to FIGS. 2A and 2B, a top level flowchart of exemplary software processes of software 12 (FIG. 1A) that can be executed on the system 10 will be described. System 10 teaches students 18 via ST reasoning in a particularly effective manner by utilizing software 12.

1) Create a logical construct - see state This act requires establishing consistent rules. 204. 2) Teach a user easy-to-understand, In one embodiment, the goals are the logically consistent goals - see process conditions to solve a puzzle. 210. Process 210 will be further described in conjunction with FIG. 4. 3) Select appropriate subject matter areas - Select the appropriate material to teach. see state 212. 4) Divide each selected subject matter into parts consisting of rules and properties. 4a) Virtual apparatus models rules and For example, shapes tightly fit holes having properties - see process 220. Process the analogous receiving shape. A penguin 220 will be further described in can only go up and down ladders, or walk on conjunction with FIG. 5. completely smooth paths. 4b) Establish error tolerances - see state 222. Some problems have no allowable error. For example, 2 + 2 = 4. No error tolerance applies. For a problem involving estimation, an appropriate error tolerance is set. 5) Teach the user to operate virtual Use simple problems as teaching tools. A apparatus - see process 230. Process special training level may serve this purpose. 230 will be further described in conjunction with FIG. 6. 6) Request the user to operate the virtual This can include requests such as “Solve apparatus to reach the pre-defined and puzzle” or “Fix success path.” pre-understood goal - see process 240. Process 240 will be further described in conjunction with FIG. 7. 7) Does the user operate the apparatus Was puzzle solved? Was success path fixed? successfully? See decision state 706 of FIG. 7. If YES go to 7a, if NO go to 7b. 7a) If YES, provide a success indicator. See These depend upon the rules established state 708 of FIG. 7. above. The possibilities are endless. A penguin could follow a path. A log or girder could bridge a gap. Ideally, this is more than a green check, or a “YES”. Ideally, more than one success indicator appears. 7aa) Preferably a success indicator illustrates This is rules and puzzle dependent. WHY user was successful. See state 710 of FIG. 7. GO TO 8. 7b) If NO, provide lack of success This is more than the lack of a success indicator. See state 712 of FIG. 7. indicator, and preferably more than a red light, a red “X” or similar. For example, a penguin cannot pass a hole or an obstruction. The path across a bridged gap has more vertical displacement than the length of the provided ladder. 7bb) Preferably lack of success indicators The lack of success indicator can be a show WHY the user was not successful. partially filled hole or an obstruction that See state 714 of FIG. 7. GO TO 8. blocks movement. The remaining gap could be beyond the ladder's reach. The amount of error is visually apparent. A hole is over filled by a number of blocks, or underfilled. A shape fits the hole in the path, but is displaced. 8) Preferably, present puzzles in a This enables positive reinforcement and substantially progressive difficulty structured success. Learner enthusiasm and sequence - see process 240. Process self image are enhanced by providing initial 240 will be further described in successes, when possible. conjunction with FIG. 7. 8a) Preferably, vary puzzle sequence This variation minimizes memorization while (through something like pseudo-random maintaining substantial benefits from the selection from a pool of puzzles in above-identified puzzle progression. appropriate bins). 9) Has user mastered the appropriate Educational theory suggests breaking mastery discipline sub-category? See decision down into appropriate sub-disciplines. state 244 of FIG. 2B. YES or NO. Certain puzzles, when combined with certain accumulated scores, or puzzle solution histories, suggest sub-category mastery. 9a) If NO, move user to next puzzle in Systematic puzzle sequencing within bins. sequence. See state 254 of FIG. 2B. 9b) If YES, user moves on to new puzzles Systematic bin sequencing. that probe new subject matter aspects. See state 250 of FIG. 2B. 9c) If subject matter area is mastered, select This selection may be fixed, result determined new subject matter area. See state 252 teacher determined, student determined, or of FIG. 2B. other. 10) The system and puzzles may be Spatial temporal reasoning may minimize, or language-free, or may use language. eliminate the need for language. Language may also be used to satisfy marketing needs and be within the method and system. 11) Language-incorporating puzzles bridge Even if the system is ST based, much of the the language gap. See state 248 and world is LA based. While the system and optionally state 246 of FIG. 2B. method teach in a ST universe, at some point, the accumulated learning received from the system is to be related by the student to a primarily LA environment. When mastery of discipline sub-category is complete, the software seamlessly introduces language to the user in the puzzle (state 248), such as via numerals, labels, etc. See the example problems/puzzles in the appendices for examples of introducing language in the puzzle. The software 12 can optionally introduce language to the user in the puzzle at state 246 when there is partial mastery of the discipline sub-category as desired.

Referring to FIG. 3, an exemplary hierarchy of subjects, aspects and puzzles is shown as an aid in understanding states 250, 252 and 254 of FIG. 2B. Subject matter areas 302 and 304 are shown as being at a first level of hierarchy; aspects 310, 312 (of subject 302), and 314 (of subject 304) are shown as being at a second level of hierarchy; and puzzles 1 to N (320) corresponding to aspect 310, puzzles 1 to N (322) corresponding to aspect 312, and puzzles 1 to N (324) corresponding to aspect 314 are shown as being at a third level of hierarchy.

Certain underlying counterintuitive techniques enhance the effectiveness of the system 10 (FIG. 1A). An underlying principle is simplifying the graphics generated by software 12 and viewed upon display 14. The progression of video games since the game PONG has taught the exact opposite. For purposes of illustration, examples are set forth in the appendices to clearly illustrate features of the system 10.

In the system 10, an animated FIG. 100, known as JiJi, appears in puzzles 22, and is both a success indicator and a lack of success indicator depending upon whether student 18 has selected a proper member of a solution set to make the success path passable, and take the puzzle from the puzzle stage to the solution stage. Of course, other animated figures can be used in other embodiments.

The version of Seed described in Appendix H has several non-obvious differences from the prior art version. First of all, the present version is self-contained, and thus does not require intervention and/or instruction by a teacher. In the prior art versions of Big Seed, and other puzzles, teacher intervention and instruction is essential to enable the puzzles to provide a learning experience. Second, at least some phases of the current puzzle are self-contained in ST space and do not require that the student receives LA space input. Third, it has been determined that the student receives a better quality learning experience when the arena stage is impoverished.

This is counterintuitive. Video games theory over the past twenty plus years has emphasized more and more graphics, and a richer video environment to attract the user's attention. Impoverishing the video environment enhances the student's learning experience, and allows students to gain maximum benefit from ST reasoning. In an impoverished environment, only essential images or output are included in an animation of the problem and puzzle and any positive or negative feedback to the user, in one embodiment. Essential images include only those images that are directly involved in the puzzle/problem and its solution. Output related to unnecessary movement on the screen, or graphics not involved in puzzle solution are not essential. Essential images are of a minimum complexity in that they contain little or no information that is not directly related to the problem. Research was conducted on a typical puzzle, identified as “bricks.” The “bricks” example shown in Appendix I demonstrates the differences between an impoverished and non-impoverished environment in the puzzle. The advantages of the impoverished environment are typical of the puzzles utilized in the system 10.

The system has great potential for assisting a wide variety of students. Specially suited student populations include pre-school students, elementary students, learning disabled students, hearing impaired students, students with low achievement levels in language arts, as well as students lacking language skills in a particular language, even though their overall LA reasoning may be average or above.

As demonstrated in research articles, it is believed that ST reasoning based puzzles may also be used to identify those possessing gifted intelligence or genius qualities. The early identification of the gifted student is essential to maximizing the inherent capacities possessed by such learners.

The system may utilize alphanumeric identifying indicia without requiring the student to utilize LA reasoning in the puzzle solution process. One or a small series of letters or numbers may well serve to identify which alternative process is employed in a multi-process puzzle. For example “GCF” or “LCM” serve as distinctive shapes easily recognized by the student, without any requirement that the student associate the symbols with particular letters or words. Other nonsense symbols could be employed. However, as ultimate integration of ST reasoning into a primarily LA world remains an ultimate goal of the system 10, utilizing alphanumeric identifying indicia can be a valuable aid in the eventual LA integration process.

Referring to FIG. 4, the process 210 previously shown in FIG. 2A will be described. Process 210 is used by system 10 to teach a user easy to understand, logically consistent goals.

Process 210 begins at a start state 402 and proceeds to state 404 to present an arena having an animated character, an obstacle and a virtual apparatus, in certain embodiments. Proceeding to state 406, process 210 teaches the students a simple goal. In certain embodiments, a goal is to get JiJi, an animated penguin 100 (FIG. 1B), to move across the display screen and past some obstacle. To meet this goal, the student knows that they have to do something. By “doing something”, they have to perform a series of mouse clicks on the right objects on the screen to remove the obstacle and make the path passable. The system 10 teaches this by starting out with the simplest games. These games can include only a single object to click on or manipulate. Proceeding to state 408, clicking on the object will cause an animation of manipulating the object to show how the obstacle is overcome so as to allow the animated character to traverse a field of the arena past the eliminated object. In certain embodiments, the obstacle is removed, and the penguin walks across the screen.

In one embodiment, such as where the user is using the system 10 for the first time, state 404 may present an arena having only a virtual apparatus. Advancing to state 406, this virtual apparatus only has a single object to click or manipulate which eliminates any distracting elements from the display and makes it easy for the user to understand what should be done.

At the completion of state 408, process 210 advances to a decision state to decide if a predetermined condition is met. In certain embodiments, the condition can be that the user manipulated the object correctly a preselected number of times. If the predetermined condition is not met, as determined at decision state 412, process 210 advances to state 412 where either the obstacle or the virtual apparatus is changed to present a new problem to the user. The user then manipulated an object in the virtual apparatus and process 210 continues at state 408. If the predetermined condition is met, as determined at decision state 412, process 210 returns at a state 414 where it is deemed that the user understands the goals taught by process 210.

Therefore, after the penguin walks across the screen, a new problem is presented. If the user doesn't click on the object, the penguin doesn't do anything. The reward is that the penguin walked across the screen, and a new puzzle is presented. The students want to see something new, and don't want to be stuck seeing the same screen of static objects in an impoverished environment. So they quickly become motivated to want to click on the appropriate spot to remove the obstacle and have the penguin “move on”.

After a sufficient number of puzzles of this type, process 210 increases the difficulty at state 412. Process 210 can add two objects that can be clicked on. Clicking on one of them (the “correct” one) will remove the obstacle, and clicking on the “wrong” one will be unsuccessful in removing the obstacle. The “wrong” clickable object is different from before where there wasn't any other clickable object at all. Clicking the “wrong” object will cause the virtual apparatus to start “working”, but it will fail to remove the obstacle (fail to make the path passable). In other words, process 210 shows why the object was the “wrong” thing to click on. Process 210 steadily increases the difficulty appropriately, such as having one clickable item to having two clickable items. Subsequently, process 210 could add more clickable items (where some are right and some are wrong). In one embodiment, process 210 could also make it so that the user has to click on a sequence of items, and only a correct sequence will “work”.

A simple example of the first two levels of difficulty is as follows:

-   -   Easy puzzle: JiJi is standing on the left side of the screen         facing to the right. The ground on which JiJi stands has a hole         in it. The hole is the shape of a rectangle. Hovering above the         ground is a clickable object in the shape of a rectangle. If the         user clicks on the clickable object, the object transitions to         the hole and fills the ground so that the path is smooth. After         this, JiJi walks across the now passable path. JiJi walks off         the right side of the screen, and a new puzzle is presented. The         next time, the puzzle can have a hole in the ground in the shape         of a triangle, and the clickable object can be an appropriately         shaped triangle to fill the hole.     -   Harder puzzle: A harder puzzle can be if the hole in the ground         is a half-circle, and there are two clickable objects hovering         in the sky. One object is an appropriately shaped half-circle         (the “right” object), and the second is a rectangle. Clicking on         the rectangle causes the rectangle to transition over to the         hole in the ground and attempt to fill it. Because the object is         the wrong shape, it will not fill the hole appropriately. It         might not fill up all the way to the surface of the walkway, or         maybe it fills too much and creates a bump in the ground.         Regardless of the type of the incorrect fill attempt, after         process 210 attempts to fill the hole, JiJi walks over to the         hole, turns and faces the user (indicating that JiJi doesn't         feel comfortable trying to pass the unsmooth path), and then         JiJi turns to the left and walks back to where JiJi started. The         user sees that this didn't get JiJi on to the next puzzle. The         user is given the same puzzle again. If the user clicks on the         half-circle object, then the hole is filled appropriately, and         JiJi is able to walk all the way across the screen and get to         the next puzzle.

The examples above of executing process 210 show how the system teaches the logically consistent goals. In certain embodiments, the goal is the get JiJi past the obstacle and on to the next problem. The condition to obtain this goal is to make the path passable. The way the user obtains this goal is by a sequence of clicks on the appropriate parts of the screen. Process 210 teaches this by starting off with very simple games as described above. Once the student understands this goal and the way to obtain this goal, the system 10 can then start teaching the subject matter, e.g., mathematics. The system does so by creating problems with the same goal (removing the obstacle so JiJi can get across the screen). In order for the user to determine the correct sequence of clicks, the user must understand the underlying mathematics that the game is trying to teach. This leads to process 220, described below.

Referring to FIG. 5, the process 220 previously shown in FIG. 2A will be described. Process 220 is used by system 10 to model rules and properties for a subject area by the virtual apparatus. In certain embodiments, the subject area is an area of mathematics. For example, “addition of integers” could be a subject area. Other examples of subject areas include: subtraction, fractions, multiplication, perimeter, graphing, and so forth.

Beginning at a start state 502, process 220 moves to state 504 to present objects in a virtual apparatus having rules corresponding to a subject matter area. The system 10 attempts to teach the subject area by modeling the subject area with a virtual apparatus. A virtual apparatus is a graphical entity presented on the computer screen that reacts to a sequence of user mouse clicks or other way of selecting or manipulating one or more spatial locations. In the simple example described earlier, the shape hovering in the sky is the virtual apparatus. In that case, the virtual apparatus consisted of one or more shapes. Clicking on the shape causes the shape to transition over to the hole in the ground and attempt to fill the hole. The action is what the apparatus is designed to do (the “rules”).

To teach a subject area, a virtual apparatus is designed that has rules which correspond to the subject area. For example, to model addition, the system can have a virtual apparatus that has different stacks of rectangles. Clicking on a particular stack causes the planks in the stack to transition over to the holes in the ground and attempt to fill them. At state 506, process 220 animates application of rules for a selected object in the virtual apparatus in a clear manner appropriate for the subject matter area. For example, to make the user do an addition problem, the arena can have two holes. One of the holes is three planks deep, and the other hole is two planks deep. If the user clicks on a stack that has only four planks, then the planks will transition over to the first hole, and successfully fill up the three planks worth deep hole. Then the remaining plank will move over to the second hole and attempt to fill it. Unfortunately, the second hole requires two planks, but there is only one left. As a result, the second hole is not filled perfectly, and JiJi is not able to cross. In this case, the user needs to click on a stack of five planks to successfully solve the puzzle. At the completion of state 506, process 220 advances to a return state 508.

The above example illustrates a simple way to model addition with a virtual apparatus. The system 10 can model all of mathematics in this way. Several game designs for mathematics are included in the appendices.

A feature of the system is that the workings of the virtual apparatus should be visually “clear” to the user as to what the virtual apparatus does. An example of an “unclear” virtual apparatus for the addition example above is as follows:

-   -   The user clicks on a stack of planks, and the stack of planks         disappear, and then reappear positioned in the holes in the         ground.

The more “clear” way for the virtual apparatus to work is as follows:

-   -   The user clicks on a stack of planks and the stack visually         transitions (not too quickly) over to the first hole in a         continuous fashion (not a single large jump, but a sequence of         movements). Once the stack of planks arrives, the stack stops,         and then one by one, the planks at the bottom of the stack move         to fill the first hole. After the first hole is filled, the         stack transitions over to the next hole and again, one by one,         the planks move into the hole.

Referring to FIG. 6, the process 230 previously shown in FIG. 2A will be described. Process 230 is used by system 10 to teach a user to operate the virtual apparatus. The user knows as a result of process 210 above that they need to remove the obstacle to allow JiJi to pass. They also know that they need to operate the virtual apparatus successfully. In order to operate the apparatus successfully, they need to learn how this particular virtual apparatus works. The system 10 teaches the user using similar acts as described above for process 210.

Beginning at a start state 602, process 230 proceeds to state 604 and presents to the user an arena having at least an animated character and an obstacle. Advancing to state 606, process 230 presents to the user a virtual apparatus having a predetermined object identified in the arena, such as by highlighting or using a pointer to identify the object. If the subject matter area is sophisticated, the virtual apparatus typically has multiple clickable regions, and can require a particular sequence of clicks to make it do the appropriate thing to remove the obstacle. If the user starts clicking randomly in the arena, it could take a long time for the user to figure out how the virtual apparatus works. Therefore, the system presents an appropriately simple problem to the user. Then, in certain embodiments, process 230 masks out all of the clickable regions of the virtual apparatus except for a first region (such as in a sequence of regions) that the user must click on in order to solve the problem. Then process 230 points out this region to the user. One way that process 230 points out the region is by highlighting it using a bright color so the user sees it clearly. Another technique is to place a hand cursor over the object to prompt the user to click on the object. Proceeding to state 608, process 230 animates the result of manipulating the identified object to show how the virtual apparatus works. Moving to a decision state 610, process 230 determines if further objects in the virtual apparatus are to be identified to the user, such as, for example if a sequence of manipulations of objects is required to make the virtual apparatus work. If further objects are to be identified, as determined at decision state 610, process 230 advances to state 612 to change the virtual apparatus to identify another predetermined object, and then shows how the virtual apparatus works at state 608, previously described. For example, process 230 can mask out all of the clickable regions except for a second region (in a sequence) that the user must click on. In essence, the system guides the user through a problem, showing the user what to click on and making it so they can only get it right by identifying the appropriate region as the only clickable region at the time. In certain embodiments, after the system guides the user through the sequence, the virtual apparatus does its function (through animation) and the user observes how it works.

After this animation, process 230 can determine that no further objects are to be identified, as determined at decision state 610. If so, process 230 can advance to optional state 614 to identify two or more predetermined objects in the virtual apparatus at the same time. For example, the system can present another problem, and unmask more clickable areas so the user has to decide on their own what to click on. The system can gradually increase the difficulty so that the user has a chance to get a feel for how to operate the virtual apparatus. Proceeding to optional state 616, process 230 animates the result of manipulating at least one of the identified objects in the virtual apparatus to show how the apparatus works. Eventually, the user knows how the apparatus works, and then must use it to solve the problems related to the subject area. Since the rules of the virtual apparatus are related to the rules of the subject area, just learning how to operate the virtual apparatus is progress towards learning the subject area.

Referring to FIG. 7, the process 240 previously shown in FIG. 2A will be described. Process 240 is used by system 10 to request students to operate the virtual apparatus to solve increasingly difficult problems. Thus, further progress is made by asking the user to operate the virtual apparatus successfully to solve new and more sophisticated problems. For example, the rules of addition are the same for small numbers and large numbers. Once the user knows how addition works, there is still a lot of learning to be done to be come adept at solving addition problems of increasing difficulty.

Beginning at a start state 702, process 240 moves to state 704 to request the user to manipulate the virtual apparatus. Proceeding to a decision state 706, process 240 determines if the user chose the correct object(s) or sequence of objects. If so, process 240 advances to state 708 to provide one or more success indicators to the user, such as via animation. Continuing at state 710, process 240 shows the user reasons why the chosen objects caused success in the problem. The appendices provide examples of states 708 and 710 for various problems. Returning to decision state 706, if the user did not choose the correct object(s) or sequence of objects, process 240 proceeds to state 712 to provide one or more lack of success indicators, such as via animation. Continuing at state 714, process 240 shows the user reasons why the chosen objects caused the lack of success in the problem.

At the completion of either state 710 or 714, process 240 checks if the problem was solved correctly. If not, process 240 continues at state 704 to request the user to manipulate the virtual apparatus as described above. In certain embodiments, the user is asked to repeat the same problem. In other embodiments, the user is asked to solve a new problem similar to the problem that was incorrectly solved. However, if the problem is correctly solved, as determined at decision state 720, process 240 advances to a decision state 722 to determine if a further problem in a sequence of problems having progressive difficulty are available. If so, process 240 continues at state 724 by selecting a new problem for the user. Proceeding to an optional state 726, process 240 can increase the difficulty in the virtual apparatus to make the problem more challenging for the user, such as, for example, by having more objects, by requiring a certain sequence of objects to be selected, and so forth. Process then continues at state 704 to request the user to manipulate the virtual apparatus, as described above. Returning to decision state 722, if a further problem in a sequence of problems having progressive difficulty is not available, such as due to all the problems being executed, process 240 moves to a return state 730.

CONCLUSION

While specific blocks, sections, devices, functions and modules may have been set forth above, a skilled technologist will realize that there are many ways to partition the system, and that there are many parts, components, modules or functions that may be substituted for those listed above.

While the above detailed description has shown, described, and pointed out the fundamental novel features of the invention as applied to various embodiments, it will be understood that various omissions and substitutions and changes in the form and details of the system illustrated may be made by those skilled in the art, without departing from the intent of the invention. 

What is claimed is:
 1. A method of academic subject training in conjunction with a computer animation executed by a computing environment including a processor and a display, the method comprising: for each of a plurality of category areas related to the academic subject, creating a logical construct including establishing a set of consistent rules, so that each of the related academic subject area categories has a corresponding and appropriate set of consistent rules; displaying, via the processor and the display, and in a graphical user interface, a virtual apparatus with virtual components that are manipulated by a user being trained; teaching the user to understand logically consistent goals by operating the virtual apparatus in an impoverished video environment and without language interaction, and providing at least one of the virtual components of the virtual apparatus which can be manipulated; modeling, via the processor, properties and the set of consistent rules for a particular one of the academic subject area categories to the user by the virtual apparatus without language interaction; teaching the user to operate the virtual apparatus without language interaction; allowing the user to operate the virtual apparatus, including manipulating the virtual components, and/or selecting answer choices defined by the virtual apparatus to reach goals in a sequence of problems having progressive difficulty and without language interaction; receiving, via the graphical user interface of the computer environment, a user input manipulating a virtual component of the virtual apparatus; determining, based at least in part on the input, and in response to the input, a transformation of the virtual components of the virtual apparatus; and automatically animating movement, on the display and in the graphical user interface, of at least some of the virtual components of the virtual apparatus according to the determined transformation and so as to indicate to a user positive or negative feedback, wherein teaching the user to understand logically consistent goals comprises animating the result of manipulating the at least one of the virtual components to show how a path is changed from impassable to passable, wherein in the impoverished video environment only essential images are included in the animation, wherein essential images include only those images directly involved in a problem and its solution, and wherein there is no output on the display not involved in a problem's solution, and wherein without language interaction relies on spatial-temporal reasoning interaction, and wherein the academic training is without intervention and instruction by a teacher, wherein the display of the virtual components includes at least one predetermined virtual component that is configured as being transformable between a displayable graphical representation and a corresponding, displayable language/symbol representation, and wherein upon meeting a criterion related to the particular one of the academic subject area categories, the at least one transformable virtual component is indicated to be transformed from the displayable graphical representation to the displayable language/symbol representation, wherein the criterion related to the particular one of the academic subject area categories includes mastery of the academic subject area category by the user while using the displayable graphical representation for the transformable virtual component(s) of the academic subject area category.
 2. The method of claim 1, additionally comprising: selecting an academic subject area category appropriate for the user; and selecting a sequence of problems according to the selected academic subject area category.
 3. The method of claim 1, additionally comprising establishing error tolerances for the problems.
 4. The method of claim 1, additionally comprising determining if the user has mastered an academic subject matter sub-category.
 5. The method of claim 4, additionally comprising introducing language elements to the user in conjunction with the computer animation if the user has mastered the academic subject matter sub-category.
 6. The method of claim 5, wherein the language elements comprise numerals and/or labels.
 7. The method of claim 1, wherein the virtual components correspond to a graphical set of possible solutions to the problems.
 8. The method of claim 1, wherein teaching the user to understand logically consistent goals comprises: displaying an arena having an animated character, an obstacle and the virtual apparatus; and animating, by the processor, a result of manipulating at least one of the virtual components.
 9. The method of claim 1, wherein the path includes an obstacle and the animating includes showing how an animated character traverses past the obstacle on the path.
 10. The method of claim 1, wherein selection of a wrong virtual component by the user causes the virtual apparatus to start working and once show a failure to achieve a goal for a particular problem.
 11. The method of claim 1, wherein the essential images are of a minimum complexity in that they contain little or no information that is not directly related to the problem.
 12. The method of claim 1, wherein the at least one virtual component has a corresponding flag that is configured to be set upon meeting the criterion related to the particular one of the academic subject area categories, wherein the transformation of a particular type of virtual component is controllable by the corresponding flag in the sequence of problems at selectable levels of training in each academic subject area category, wherein the sequence of problems at the levels of training in each academic subject area category includes a plurality of different animations configured to be displayed on the display.
 13. The method of claim 1, wherein when a transformable virtual component is displayed in the form of the displayable language/symbol representation on the display for one or more subsequent problems in the sequence of problems, the transformable virtual component is transformed back to the displayable graphical representation and is displayed in the form of the displayable graphical representation on the display during animations in the one or more subsequent problems.
 14. The method of claim 1, wherein the answer choices are defined by the virtual apparatus as one or more clickable objects or regions related to the virtual components.
 15. The method of claim 1, wherein the displayable language/symbol representation of the at least one predetermined virtual component represents part of a mathematical expression.
 16. The method of claim 1, additionally comprising: identifying one or more of the virtual components as being transformable between a displayable graphical representation and a corresponding displayable language/symbol representation separately for each academic subject area category; and wherein upon meeting a criterion related to a particular one of the academic subject area categories, determining which of the identified transformable virtual components is to be transformed from the displayable graphical representation to the displayable language/symbol representation and to be displayed in the form of the displayable language/symbol representation, wherein the criterion related to the particular one of the academic subject area categories includes mastery of the academic subject area category while using the displayable graphical representation for the identified virtual components of the academic subject area category.
 17. A method of academic subject training via a computer animation operating in a virtual computing environment, the method comprising: performing a first computer animation indicative of a mathematically dependent task in an impoverished video environment, wherein the first computer animation is executed by a computing environment having a display; performing a second computer animation displayed on the display, wherein the second computer animation comprises a display of a multiple step problem and the presentation of a virtual apparatus with virtual components to model properties for a particular academic subject area and to accomplish the mathematically dependent task; receiving input, via the impoverished video environment, indicative of user manipulation of the virtual apparatus executing in the computing environment so as to solve the multiple step problem, wherein the first and second computer animations are performed without language interaction; determining, based at least in part on the input, and in response to the input, a transformation of the virtual components of the virtual apparatus; and automatically animating movement, on the display, of at least some of the virtual components of the virtual apparatus according to the determined transformation and so as to indicate to a user positive or negative feedback relevant to the academic subject matter and the user's manipulations if the multiple step problem was, or was not solved correctly, wherein the academic training is without intervention and instruction by a teacher, wherein in the impoverished video environment only essential images are included in the animation, wherein essential images include only those images directly involved in a problem and its solution, and wherein there is no output on the display not involved in a problem's solution, and wherein the first and second displayed animations rely on spatial-temporal reasoning interaction of the user with at least one of the virtual components in the virtual apparatus, wherein the display of the virtual components includes at least one virtual component that is configured as being transformable between a displayable graphical representation and a corresponding displayable language/symbol representation, and wherein upon meeting a criterion related to a category of the particular academic subject area, the transformable virtual component is indicated to be transformed from the displayable graphical representation to the displayable language/symbol representation, wherein the criterion related to the category of the particular academic subject area includes mastery of the academic subject area category by the user while using the displayable graphical representation for the transformable virtual component of the academic subject area category.
 18. The method of claim 17, wherein animating positive feedback comprises showing the user why the multiple step problem was solved correctly.
 19. The method of claim 18, wherein showing the user why the multiple step problem was solved correctly comprises animating application of a selected correct solution from a discrete set of solutions to a path in an arena.
 20. The method of claim 17, additionally comprising introducing language elements to the user in conjunction with the computer animation.
 21. The method of claim 20, wherein the language elements comprise numerals and/or labels.
 22. The method of claim 20, wherein the language elements are added to the display near the virtual apparatus.
 23. The method of claim 20, wherein the language elements are indicative of portions of the virtual apparatus and are added to the display in place of portions of the virtual apparatus.
 24. The method of claim 20, additionally comprising solving a new problem in a language-analytic computing environment without the spatial-temporal interactions.
 25. The method of claim 17, wherein animating negative feedback comprises showing the user why the problem was not solved correctly.
 26. The method of claim 25, wherein showing the user why the multiple step problem was not solved correctly comprises animating application of a selected incorrect solution from a discrete set of solutions to a path in an arena and visually indicates that the virtual apparatus will function incorrectly to attempt solving the multiple step problem.
 27. The method of claim 17, wherein the method of training is self-contained.
 28. The method of claim 17, wherein solving the problem teaches the user to utilize spatial temporal reasoning.
 29. The method of claim 17, additionally comprising designating a task to be performed in the computer animation.
 30. The method of claim 17, wherein the computer animation includes only essential images.
 31. The method of claim 30, wherein essential images are images that are only directly involved in the problem and its solution.
 32. The method of claim 17, wherein the positive feedback computer animation includes only essential output.
 33. The method of claim 32, wherein essential output is graphical output only directly involved in a solution of the problem.
 34. The method of claim 17, wherein the negative feedback computer animation includes only essential output.
 35. The method of claim 17, wherein animating positive feedback comprises having an animated character traverse a horizontal path in an arena, wherein the path is completed by solving the multiple step problem, and showing proper use of the virtually manipulated apparatus, wherein animating positive feedback is illustrative of logic required to accomplish the task and solve the multiple step problem.
 36. The method of claim 17, wherein animating negative feedback comprises having an animated character partially traverse a path up to an obstacle in an arena, and showing improper use of the virtually manipulated apparatus.
 37. The method of claim 17, wherein the virtual apparatus comprises virtual components corresponding to a graphical set of possible solutions, including a correct solution, to the multiple step problem, and the received input is indicative of manipulation of one of the set of possible solutions.
 38. The method of claim 17, additionally comprising: determining when a user has mastered an academic concept being taught by the training; and adding language elements into the computer animation when mastery has been achieved.
 39. The method of claim 17, wherein the at least one virtual component has a corresponding flag that is configured to be set upon meeting the criterion related to the particular academic subject area, wherein the transformation of a particular type of virtual component is controllable by the corresponding flag in a sequence of problems at selectable levels of training in each academic subject area, wherein the sequence of problems at levels of training in each academic subject area includes a plurality of different animations configured to be displayed on the display.
 40. The method of claim 17, wherein when a transformable virtual component is displayed in the form of the displayable language/symbol representation on the display for one or more subsequent problems in a sequence of problems, the transformable virtual component is transformed back to the displayable graphical representation and is displayed in the form of the displayable graphical representation on the display during animations in the one or more subsequent problems.
 41. A method of self-contained academic subject training executed by a computing environment including a processor and a display, without intervention and instruction by a teacher, and without language interaction, the method comprising: performing a first computer animation indicative of a mathematically dependent task in an impoverished video environment, wherein the first computer animation is executed by a processor in the computing environment; performing a second computer animation displayed on the display, wherein the second computer animation comprises a display of a multiple step problem and the presentation of a virtual apparatus to model properties of, and to accomplish, the mathematically dependent task; receiving a user input, via the impoverished video environment, indicative of a solution to the multiple step problem using a virtual apparatus with virtual components displayed in the first and second computer animations, wherein the virtual apparatus comprises a graphical entity presented on the display that responds to one or more manipulations by a user of one or more of the virtual components according to rules corresponding to the mathematically dependent task; determining, based at least in part on the input, and in response to the input, a transformation of the virtual components of the virtual apparatus; and automatically displaying, on the display, a third computer animation indicating movement of at least some of the virtual components according to the determined transformation so as to indicate feedback that shows the user why the problem was or was not solved correctly in conjunction with the sequence of user manipulations of the virtual components previously received without intervention and instruction by a teacher, and without language interaction, wherein in the impoverished video environment only essential images are included in the animation, wherein essential images include only those images directly involved in a problem and its solution, and wherein there is no output on the display not involved in a problem's solution, and wherein the first, second and third animations rely on display of spatial-temporal reasoning interactions in place of language interactions, wherein the display of the virtual components includes at least one virtual component that is configured as being transformable between a displayable graphical representation and a corresponding displayable language/symbol representation, and wherein upon meeting a criterion related to a category of a particular academic subject area, the transformable virtual component is indicated to be transformed from the displayable graphical representation to the displayable language/symbol representation, wherein the criterion related to the category of the particular academic subject area includes mastery of the academic subject area category by the user while using the displayable graphical representation for the transformable virtual component of the academic subject area category.
 42. The method of claim 41, wherein selection of a wrong virtual component by the user causes the virtual apparatus to start working and show a failure to achieve a goal. 